Metropolis, Slice or Gibbs sampling tend to be inefficient when applied in high dimensions due to their local random walk behaviour. Hamiltonian Monte Carlo (HMC) was developed around a geometrical understanding of the target distribution, borrowing concepts from physics to generate transitions and exploring the target distribution. Ultimately, moving more rapidly through the target distribution. HMC is also often the basis for implementations of MCMC algorithms such as in STAN or PyMC3.In this talk we’ll motivate and introduce the algorithm itself, its benefits but also its shortcomings.
A Conceptual Introduction to Hamiltonian Monte Carlo,
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice. Unfortunately, that understanding is confined within the mathematics of differential geometry which has limited its dissemination, especially to the applied communities for …